Analytical series expressions for the self- and mutual inductances of two-dimensional coils in the form of partial sectors

Pulsed power generators of the drum type utilize radial components of magnetic fields created by field coils located on a rotor to induce voltage on stator coils located at larger radii. Conventionally, two-dimensional (2-D) field analyses are used, and further, the field is expressed as a harmonic series and the fundamental part of the radial field is used for initial designs. Analytical series expressions for 2-D potentials and fields are utilized in this paper to derive analytical series expressions for the self-inductances and mutual inductances between the rotor and stator coils in the shape of partial sectors. The magnitudes of higher order terms are compared with that of the fundamental component. The effects of parameters such as the aspect ratios of conductor sections on the inductances and coupling constants are evaluated.